Visa for Miami for Indian passport holder with indefinite leave to remain in UK

A friend of mine has an Indian passport with indefinite leave to remain in the UK and is hoping to travel to Miami in the third week of January. I am pretty sure that he would need a visa, but was wondering:

1) Which one?
2) Where would he get his visa from? (he's based in London)
3) How long it would take to get his visa?